This invention pertains, in general, to making analog form playbacks from digitally recorded data (e.g., seismic data) which has been digitized from wide dynamic amplitude range analog form data signals initially generated by transducers, such as geophones in response to acoustically induced seismic disturbances; and, in particular, to the making of analog form playbacks such as oscillograms (or wiggle traces as they are often called by those engaged in seismic work) which are approximate, but very useful, reproductions in compressed range of the wide dynamic range amplitude-versus-time characteristic curves of the analog signal initially generated by the aforesaid transducers or geophones.
For example, in seismic exploration work each acoustically driven geophone generates wide dynamic amplitude range signals in analog form. When such signals are processed through a digital seismic recording system of the type disclosed in the patents and patent application hereinafter identified there is produced a high fidelity record, in digital form, covering the wide dynamic range of amplitudes of the signals. The reason that the digital form record is referred to herein as a high fidelity record is because the signal amplitudes are recorded accurately throughout their wide dynamic range; e.g., many binary bit positions are used to accurately record the highest signal amplitudes as well as the lowest where the range (i.e., the ratio of highest amplitudes to the lowest) may be of the order of 10.sup.6. The invention hereinafter disclosed provides methodology and apparatus for making analog form oscillograms, or wiggle traces, from the recorded digital data. The oscillograms, or wiggle traces, are of relatively lower fidelity than the aforementioned digitally recorded data. Although, said oscillograms are of relatively lower fidelity, serious distortions are, nevertheless, not introduced in reconverting the digital data to analog form data.
The recordation in digital form of wide dynamic amplitude range analog form signals initially generated by geophones is disclosed in, among others, the following: U.S. Pat. No. 3,241,100, granted Mar. 15, 1966 in behalf of R. J. Loofbourrow and entitled "Digital Seismic Recording System"; U.S. Pat. No. 3,264,574, granted Aug. 2, 1966, in behalf of R. J. Loofbourrow and entitled "Amplifier System"; and, U.S. Patent Application Ser. No. 786,706 now U.S. Pat. No. 3,603,972, filed Dec. 24, 1968 in behalf of James R. Vanderford and entitled "Amplifier System".
Although the invention is hereinafter described as being employed in conjunction with digital seismic recording systems such as those disclosed in the patents and patent application hereinbefore identified it is, nevertheless, to be understood that the invention's field of use is not limited to seismic data processing.
As is disclosed in the patents and patent application herein disclosed the problem solved is the problem of accurately recording seismic data which is analog form has a dynamic range of amplitudes which is extremely wide. For example, a typical analog signal level for a reflection siesmic record runs from several volts of amplitude at its maximum, at the early shock portion of the record, to less than a single microvolt at the end of the seismic record when very low amplitude seismic disturbances are detected. To put it very generally, the aforementioned patents and patent application solve the problem by converting the wide dynamic amplitude range analog signals to digital form. When converted to digital form, occupying a relatively large number of binary bit positions, the full dynamic amplitude range of the analog signal initially generated by a geophone is preserved in recorded form on magnetic tape. Advantageously, the magnetically recorded digital data may subsequently be delivered to an electronic computer for further processing. Some ways and some purposes for which such digital data is subsequently processed in an electronic computer are disclosed in an article "Tools for Tomorrow's geophysics" by Milton B. Dobrin and Stanley H. Ward, published in the journal "Geophysical Prospecting", Vol. X, pages 433-452 (1962).
In the aforementioned patent application of Vanderford there is described a system wherein portions of an analog signal are converted to digital words where each digital word occupies a number of binary bit positions. Moreover, each such digital word is recorded in a floating point form. Advantageously, the floating point form, or notation, allows greater flexibility of operation and easier handling of numbers differing greatly from each other in magnitude. (See, for example, the textbook "Digital Computer Primer" by E. M. McCormick, 1959, published by McGraw-Hill Book Co., Inc., beginning at page 152). In the system disclosed in the Vanderford patent application, hereinbefore identified, a floating point digital number, or word, in the form of a mantissa and an exponent is recorded on magnetic tape. The floating point digital number represents the instantaneous absolute seismic voltage amplitude as it enters the floating point amplifier system disclosed by Vanderford. The dynamic range of the floating point digital number, or word, may be in excess of 200 db, if necessary, to cover the dynamic amplitude range of input signals (equivalent of a 36 binary bit digital number, or word). As a specific example, the floating point word as set forth in conventional algebraic form is as follows: EQU Q.sub.1 =.+-.AG.sup.-E (Equation 1)
where Q.sub.1 represents the absolute magnitude or amplitude of the floating point word; A represents the mantissa, or argument, portion of the word; G represents the base of the number system used (G=10 in the decimal, or base 10, system or G=8 is the octal system); and E represents the exponent.
As is suggested in the Vanderford patent application the floating point digital word is in the form: EQU Q.sub.2 =.+-.A8.sup.-E (Equation 2)
where Q.sub.2 represents the absolute magnitude of the amplitude of the input signal to an arrangement of amplifiers, each of which has a gain of eight (8) and, hence, the base G in equation 1 becomes an 8 in equation 2; the mantissa A represents the output amplitude of a particular amplifier in the aforesaid arrangement; and E, the exponent, represents the number of amplifier stages of gain of 8 through which the input signal has passed.
In order to record the floating point digital word of equation 2 in a binary register with, for example, 144 db of dynamic range and 14 bit accuracy, 18 bit positions would be required where the mantissa A is represented in binary form (i.e., where the radix, or base, of such a number system is 2) and where the exponent E is also represented in binary form. Of the 18 bits required: 1 bit represents the sign, allowing for bipolar input-output capabilities; 14 bits represent the mantissa; and 3 bits represent the exponent.
Although there are many advantages (some of which are set forth in the aforementioned published article of Dobrin and Ward) to recording seismic signals in digital form there still remains the need to make available to a seismic prospector a visible record of the seismic data, or portions of it. Conventionally, the visible record is an oscillogram, or wiggle trace as it is often called by seismic prospectors. Often, it is desirable for a seismic prospector in a siesmic field crew in a remote location from a main data processing center to take a quick look at a portion of the seismic data from time to time; i.e., look at wiggle traces. For example, a seismic prospector may wish to make some interpretations with respect to the wiggle trace data after coordinating such data with geological data.
The invention, hereinafter disclosed and illustrated in the accompanying drawing figures, is particularly concerned with converting the recorded digital data to the familiar wiggle trace form on recording paper. The recording paper allows about 40 db dynamic amplitude range while the digitally recorded floating point word may have a dynamic range of 156 db, or more. Thus, in converting from digital form to a practical analog form selective amplification and/or attenuation of the various amplitudes must occur. In such a conversion distortion is necessarily introduced. However, the methodology of the present invention minimizes such distortions and, as a result, there is provided analog form data in the form of oscillograms, or wiggle traces, which provide useful information to seismic prospectors, among others.